Prediction method and system for axial compression stress-strain relation of coal gangue aggregate concrete

Abstract

The invention provides a prediction method and system for an axial compressive stress-strain relation of coal gangue aggregate concrete, and belongs to the field of coal gangue aggregate concrete. The method aims at solving the problems that an existing prediction model for the axial compressive stress-strain relation of coal gangue aggregate concrete is obtained based on limited test data regression, but the physical property difference of coal gangue is large, the mechanism is complex, and the universality of the prediction model is difficult to guarantee. According to the method, an elastic modulus correction coefficient, a peak strain correction coefficient and a descending section shape parameter correction coefficient are introduced into an existing concrete axial compression stress-strain formula, and then a coal gangue aggregate concrete descending section shape parameter prediction model is deduced and established based on a two-phase composite material theory and a fault zone theory. The model is used for describing the deformability of the coal gangue aggregate concrete, and finally a prediction model of the axial compressive stress-strain relation of the coal gangue aggregate concrete is obtained; the method can effectively solve the problems of large physical property difference and complex mechanism of the coal gangue, and has universality.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of coal gangue aggregate concrete, in particular to a prediction method and system for the axial compression stress-strain relationship of coal gangue aggregate concrete. BACKGROUND

[0002] In the process of coal development and utilization, a large amount of coal gangue is produced, which is a low-calorific-value mineral by-product separated in the mining and washing process, and its production usually accounts for 10% to 25% of the raw coal output, which has become a key object in the field of industrial solid waste treatment in China. By crushing and screening process, coal gangue raw materials can be processed to produce coal gangue aggregate of different particle sizes. Using coal gangue aggregate to replace natural sandstone to prepare coal gangue aggregate concrete not only can improve the resource utilization value of coal gangue, effectively alleviate the land occupation and environmental pollution caused by coal gangue, but also can reduce the development intensity of natural sandstone resources, which has double benefits for balancing the demand of urban construction and ecological environment protection.

[0003] At present, the research on the axial compression stress-strain relationship of coal gangue aggregate concrete is still in its infancy, and the existing prediction models of the axial compression stress-strain relationship of coal gangue aggregate concrete are all based on the regression of limited experimental data. However, the physical properties of coal gangue are quite different, and the influencing mechanism of the axial compression stress-strain relationship of coal gangue aggregate concrete is complex, so it is difficult to ensure the universality of the prediction model based on experimental regression. SUMMARY

[0004] The technical problem to be solved by the present application is:

[0005] To solve the problem that the existing prediction models of the axial compression stress-strain relationship of coal gangue aggregate concrete are all based on the regression of limited experimental data, but the physical properties of coal gangue are quite different, and the influencing mechanism is complex, which makes it difficult to ensure the universality of the prediction model.

[0006] The technical scheme adopted by the present application to solve the above technical problem is:

[0007] The present application provides a prediction method for the axial compression stress-strain relationship of coal gangue aggregate concrete, comprising the following steps:

[0008] S100, introducing an elastic modulus correction coefficient k in the axial compression stress-strain relationship formula c,E , a peak strain correction coefficient k c,ε and a descending segment shape parameter correction coefficient k c,α to obtain an axial compression stress-strain relationship model of coal gangue aggregate concrete;

[0009] S200, for the elastic modulus correction coefficient k c,E, the relationship between the elastic modulus of the coal gangue aggregate concrete and the elastic modulus of the ordinary concrete with the same mix proportion is obtained;

[0010] S300, the peak strain correction coefficient k c,ε , based on the Voigt model in the two-phase composite material theory, the relationship between the peak strain of the concrete and the peak strain of each component in the concrete is obtained, and the calculation formula of the peak strain correction coefficient k c,ε of the coal gangue aggregate concrete is derived;

[0011] S400, the descending segment shape parameter correction coefficient k c,α , the relationship between the fracture energy of the coal gangue aggregate concrete and the fracture energy of the ordinary concrete is established to determine the descending segment shape parameter correction coefficient k c,α ; in order to calculate the fracture energy, a fracture zone width prediction model of the coal gangue aggregate concrete is constructed to obtain the calculation formula of the fracture zone width correction coefficient of the coal gangue aggregate concrete; the apparent density of the weighted average is calculated by using the volume ratio of the coal gangue coarse aggregate, the coal gangue fine aggregate and the natural coarse aggregate and the natural fine aggregate in the concrete, and finally the calculation formula of the descending segment shape parameter correction coefficient k c,α .

[0012] Further, in step S100, the elastic modulus correction coefficient k c,E , the peak strain correction coefficient k c,ε and the descending segment shape parameter correction coefficient k c,α are introduced, as shown in formulas (1)-(3):

[0013]

[0014] wherein, respectively represent the elastic modulus of the coal gangue aggregate concrete and the ordinary concrete;

[0015]

[0016] wherein, respectively represent the peak strain of the coal gangue aggregate concrete and the ordinary concrete;

[0017]

[0018] wherein, respectively represent the descending segment shape parameter of the coal gangue aggregate concrete and the ordinary concrete;

[0019] The elastic modulus correction coefficient k c,E , the peak strain correction coefficient k c,ε and the descending segment shape parameter correction coefficient kc,α Substituting into the concrete axial compressive stress-strain relationship model, the axial compressive stress-strain relationship model of the coal gangue aggregate concrete is obtained, which is expressed by formula (4) to formula (8):

[0020]

[0021]

[0022]

[0023] Wherein, σ represents the axial compressive stress of the coal gangue aggregate concrete, and ε represents the axial compressive strain of the coal gangue aggregate concrete. σf represents the peak stress of the coal gangue aggregate concrete.

[0024] Further, in step S200, for the elastic modulus correction coefficient k c,E :

[0025]

[0026] Wherein, r CGCA is the replacement rate of the coal gangue coarse aggregate, r CGFA is the replacement rate of the coal gangue fine aggregate, is the volume fraction of the coal gangue coarse aggregate in the total aggregate; is the volume fraction of the coal gangue fine aggregate in the total aggregate; is the volume fraction of the total aggregate in the concrete.

[0027] Further, in step S300, for the ordinary concrete, the peak strain is expressed by the peak strain of the aggregate and the peak strain of the cement paste and the volume fraction of the aggregate:

[0028]

[0029] In the formula, respectively represent the peak strain of the aggregate and the peak strain of the cement paste when the axial stress reaches the peak stress of the ordinary concrete; V NA represents the volume fraction of the total aggregate in the concrete;

[0030] The peak strain of the coal gangue aggregate concrete when the axial stress reaches the peak stress can also be expressed by the peak strain of the total aggregate in the coal gangue aggregate concrete and the peak strain of the cement paste and the volume fraction of the total aggregate:

[0031]

[0032] In the formula, respectively represent the peak strain of the total aggregate and the cement paste when the axial stress reaches the peak stress of the coal gangue aggregate concrete; represents the volume fraction of the total aggregate in the coal gangue aggregate concrete;

[0033] In the loading process of the concrete, the aggregate does not undergo plastic deformation, so and are calculated by formula (14) and formula (15) respectively:

[0034]

[0035]

[0036] wherein, represents the peak stress of the ordinary concrete; represents the stiffness of the aggregate in the ordinary concrete, i.e. the elastic modulus of the natural aggregate in the ordinary concrete; represents the peak stress of the coal gangue aggregate concrete; represents the stiffness of the total aggregate in the coal gangue aggregate concrete, i.e. the elastic modulus of the total aggregate in the coal gangue aggregate concrete;

[0037] wherein the total aggregate in the coal gangue aggregate concrete is a two-phase composite material of the natural aggregate and the coal gangue aggregate, and the stiffness thereof is calculated according to formula (16):

[0038]

[0039] wherein, CGA is the elastic modulus of the coal gangue aggregate, is the volume fraction of the natural aggregate in the total aggregate in the coal gangue aggregate concrete;

[0040] Since the peak strain of the cement paste has a significant linear correlation with the peak stress thereof, it is approximately represented by formula (17):

[0041]

[0042] wherein, represents the peak stress of the cement paste; represents the peak strain of the cement paste, and ;

[0043] Finally, the coal gangue aggregate is replaced with the natural aggregate in the same volume to obtain the expression of the peak strain correction coefficient of the coal gangue aggregate concrete, as shown in formula (18):

[0044]

[0045] Further, in step S400, a fracture energy calculation model of the ordinary concrete is established based on the fracture zone width of the ordinary concrete :

[0046]

[0047] wherein, represents the fracture zone width of the ordinary concrete; represents the elastic modulus of the ordinary concrete; represents the tensile strain softening modulus of the ordinary concrete; represents the tensile strength of the ordinary concrete;

[0048] Assuming that the ratio of the elastic modulus to the tensile strain softening modulus of the coal gangue aggregate concrete is equal to that of the ordinary concrete ; thus, a calculation model of the fracture energy of the coal gangue aggregate concrete is established as follows:

[0049]

[0050] wherein, represents the fracture zone width of the coal gangue aggregate concrete; represents the elastic modulus of the coal gangue aggregate concrete; represents the tensile strength of the coal gangue aggregate concrete;

[0051] Dividing equation (20) by equation (19), the fracture energy amplification factor of the coal gangue aggregate concrete is obtained as follows: as shown in equations (21)-(23):

[0052]

[0053]

[0054] wherein, k c,d represents the fracture zone width correction factor of the coal gangue aggregate concrete; k c,ft represents the tensile strength correction factor of the coal gangue aggregate concrete; k c,E represents the elastic modulus correction factor of the coal gangue aggregate concrete;

[0055] Based on the fact that the maximum particle size of the coarse aggregate in the concrete affects the fracture zone width of the concrete by affecting the development path of the crack, a fracture zone width prediction model of the coal gangue aggregate concrete is established as follows:

[0056]

[0057] wherein, represents the reference apparent density of the concrete; ​ρ x represents apparent density of ordinary concrete and coal gangue aggregate concrete; X1, X2 represent regression coefficients; ρ x represents maximum particle size of coarse aggregate in ordinary concrete; ρ x represents maximum particle size of coarse aggregate in coal gangue aggregate concrete;

[0058] Further, we get:

[0059]

[0060] When the coarse aggregate in ordinary concrete and coal gangue aggregate concrete uses the same mix proportion, it is considered that the maximum particle size of the coarse aggregate is similar, that is, ≈1, then formula (26) is simplified as formula (27):

[0061]

[0062] Since the coal gangue aggregate concrete and the ordinary concrete use the same mix proportion, and the coal gangue aggregate in the coal gangue aggregate concrete replaces the natural aggregate in the form of volume replacement, the aggregate volume and the cement paste volume of the two are equal, then formula (25) is obtained:

[0063]

[0064] In the formula, ρ x represents weighted apparent density of aggregate in ordinary concrete; ρ x represents weighted apparent density of aggregate in coal gangue aggregate concrete; ρ cp ρ x represents apparent density of cement paste; ρ x represents volume fraction of aggregate in concrete;

[0065] Considering that the ratio of the weighted apparent densities of the aggregates approximately replaces the ratio of the apparent densities of the concretes, the expression of the correction coefficient of the fracture zone width of the coal gangue aggregate concrete is finally obtained, as shown in formula (29):

[0066]

[0067] In the formula, X3 represents a regression coefficient;

[0068] Considering the replacement rates of the coal gangue coarse aggregate and the coal gangue fine aggregate, the weighted apparent density of the aggregate in the coal gangue aggregate concrete is calculated, as shown in formula (30)-formula (32); when the replacement rates of the coal gangue coarse aggregate and the coal gangue fine aggregate are both 0%, the weighted apparent density of the aggregate in the ordinary concrete is calculated by formula (30):

[0069]

[0070] In the formula, ρ CGCA , ρ NCARepresent the apparent density of coal gangue coarse aggregate, natural coarse aggregate; rho CGFA , rho NFA Represent the apparent density of coal gangue fine aggregate, natural fine aggregate;

[0071] Finally, the calculation expression of the concrete descending segment shape parameter is:

[0072]

[0073] A coal gangue aggregate concrete axial compression stress-strain relationship prediction system has program modules corresponding to the above steps, and executes the steps in the above application to improve the heuristic static path planning method of the mobile robot.

[0074] A computer readable storage medium stores a computer program, and the computer program is configured to realize the steps of a coal gangue aggregate concrete axial compression stress-strain relationship prediction method when called by a processor.

[0075] Compared with the prior art, the beneficial effects of the present application are:

[0076] The present application discloses the influence mechanism of coal gangue coarse aggregate and fine aggregate by carrying out single-doped, double-doped coal gangue coarse aggregate and fine aggregate concrete axial compression stress-strain relationship test, including the influence of coal gangue coarse aggregate replacement rate (0% and 100%) and coal gangue fine aggregate replacement rate (0% and 100%) on the mechanical performance indexes of concrete peak stress, transverse deformation coefficient, peak strain and deformation capacity. It can be seen from the test results that the coal gangue aggregate has a significant influence on the rising segment shape, peak strain and descending segment shape of the axial compression stress-strain relationship curve of the concrete, which is not disclosed in the existing coal gangue concrete axial compression stress-strain relationship. In order to consider the above influences, the present application introduces the elastic modulus correction coefficient k c,E , the peak strain correction coefficient k c,ε and the descending segment shape parameter correction coefficient k c,α The above three correction directions and correction coefficients are not mentioned in the existing method, and can effectively deal with the problem of large difference in coal gangue physical properties and complex mechanism, and have universality.

[0077] Based on the introduction of the above three correction coefficients, the coal gangue aggregate concrete descending segment shape parameter prediction model is established based on the two-phase composite material theory and the fracture zone theory, to describe the deformation capacity of the coal gangue aggregate concrete, and finally the coal gangue aggregate concrete axial compression stress-strain relationship prediction model is obtained. According to the test verification, compared with the collected test data, the determination coefficient R 20.95 and 0.96 respectively, which proves that the prediction model for the axial compression stress-strain relationship proposed in the application has high prediction accuracy, and further embodies the effectiveness of the mechanism research of the application. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 A flow chart of a prediction method for the axial compression stress-strain relationship of coal gangue aggregate concrete in an embodiment of the application;

[0079] Figure 2 A test device diagram for the axial compression stress-strain relationship in an embodiment of the application;

[0080] Figure 3 A typical constitutive curve diagram of a concrete test piece in an embodiment of the application;

[0081] Figure 4 A failure mode diagram of a typical test piece in an embodiment of the application;

[0082] Figure 5 A peak stress comparison diagram of concrete test pieces under different water-cement ratios in an embodiment of the application;

[0083] Figure 6 A transverse deformation coefficient development curve diagram of a concrete test piece in an embodiment of the application;

[0084] Figure 7 A peak strain comparison diagram of concrete test pieces under different water-cement ratios in an embodiment of the application;

[0085] Figure 8 A deformation capacity comparison diagram of concrete test pieces under different water-cement ratios in an embodiment of the application;

[0086] Figure 9 A Voigt model diagram in a two-phase composite material in an embodiment of the application;

[0087] Figure 10 A comparison diagram of the peak strain prediction results and the test results of coal gangue aggregate concrete in an embodiment of the application;

[0088] Figure 11 A comparison diagram of the deformation capacity predicted by the model of the application and the existing test results in an embodiment of the application;

[0089] Figure 12 A comparison diagram of the axial compression constitutive curve of concrete predicted by the model of the application and the axial compression constitutive curve of concrete predicted by Zhang et al. in an embodiment of the application;

[0090] Figure 13 A comparison diagram of the axial compression constitutive curve of concrete predicted by the model of the application and the axial compression constitutive curve of concrete predicted by Zhou et al. in an embodiment of the application;

[0091] Figure 14 The concrete axial compression constitutive curve predicted by the model of the present application in the embodiment of the present application and the concrete axial compression constitutive curve predicted by the model of Zhang et al. Comparison chart of test results;

[0092] Figure 15 The concrete axial compression constitutive curve predicted by the model of the present application in the embodiment of the present application and the concrete axial compression constitutive curve predicted by the model of Liu et al. Comparison chart of test results;

[0093] Figure 16 The concrete axial compression constitutive curve predicted by the model of the present application in the embodiment of the present application and the concrete axial compression constitutive curve predicted by the model of Dong et al. Comparison chart of test results;

[0094] Figure 17 Comparison chart of the concrete axial compression constitutive curve predicted by the model of the present application in the embodiment of the present application and the test results of the present application. DETAILED DESCRIPTION

[0095] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0096] In order to reveal the influence mechanism of coal gangue coarse aggregate and coal gangue fine aggregate, firstly, the axial compression stress-strain relationship test of concrete mixed with coal gangue coarse aggregate and coal gangue fine aggregate is carried out.

[0097] Test method

[0098] Under different water-cement ratios, the influence law of coal gangue coarse aggregate and coal gangue fine aggregate replacement rate on the axial compression stress-strain relationship curve characteristics of concrete is studied. In this test, water-cement ratio and coal gangue coarse aggregate and coal gangue fine aggregate replacement rate are the main parameters for test, a total of 8 groups of test pieces, 24 100mmx100mmx300mm prism test blocks, the mix proportion and test piece naming method are shown in detail in Table 1. .

[0099] Table Unit volume concrete mix proportion

[0100]

[0101] Wherein, the test piece number contains four elements: 1) NAC represents ordinary concrete, and CGAC represents coal gangue aggregate concrete; 2) C represents coarse aggregate, and F represents fine aggregate; 3) the suffix value after C and F represents the replacement rate of coal gangue aggregate; 4) the last number represents the water-cement ratio. Taking the typical test piece CGAC-C50-F50-0.35 as an example, the replacement rates of coarse and fine coal gangue aggregates of the coal gangue aggregate concrete test piece are both 50%, and the water-cement ratio is 0.35. CGCA r represents the replacement rate of coarse coal gangue aggregate, CGFA NFA represents natural fine aggregate; CGCA represents coarse coal gangue aggregate; and CGFA represents fine coal gangue aggregate.

[0102] The axial compression stress-strain relationship test was performed on a 500t hydraulic servo press, and the specific test device is shown in Figure 2 . In order to accurately measure the descending segment of the axial compression stress-strain relationship curve, it is necessary to increase the stiffness of the test device, so two rigid elements are symmetrically arranged on both sides of the test piece. A 100mm longitudinal strain gauge is arranged in the middle of each surface of the test piece to measure the longitudinal strain of the test piece, so as to realize physical centering during preloading; an 80mm transverse strain gauge is arranged in the middle of each surface of the test piece to measure the transverse strain of the test piece. The LVDT (displacement meter) fixed on both sides of the test piece is used to measure the axial displacement of the test piece in the descending segment, so as to prevent the strain gauge from failing due to small range (about 10000με). In this test, a 1000kN range force sensor is used for real-time monitoring of the axial load, and the transverse and longitudinal strain data are synchronously collected by combining the Teste TST3827E dynamic and static signal test analysis system, so as to obtain the load-deformation relationship of the test piece under axial compression.

[0103] The displacement control loading mode is adopted in this test, and the loading system is set as follows: keep a uniform speed of 0.5mm / min during the stage when the load does not reach 80% of the estimated peak load, and switch to a low speed of 0.1mm / min after reaching 80% of the estimated peak load until the test piece is destroyed. In order to reduce the influence of virtual displacement on the test results, the test piece is preloaded three times with 1 / 3 of the estimated peak load, and physical centering is performed at the same time, so as to ensure that the strains of each surface of the test piece are close, thereby maintaining the axial compression state. When reaching 50% of the estimated peak load, the two rigid elements will hold the load together with the test piece, so as to obtain the descending segment curve of the test piece.

[0104] Test results

[0105] 1 Loading whole process and test piece failure mode

[0106] The whole loading process and the failure mode of each concrete test piece were observed. Figure 3The axial stress-strain(σ-ε) curves of NAC-0.35 specimen and CGAC-C100-F100-0.35 specimen are selected as representatives to describe the whole loading process. In the figure, f c is the axial compressive strength of the specimen.

[0107] All specimens show no obvious damage in the initial loading stage of σ≤0.75f c . When the axial compressive stress σ exceeds 0.75f c , the longitudinal micro-cracks appear in the middle of the specimen. With the increase of load, the cracks tend to expand to the ends of the specimen. When the axial compressive stress σ reaches f c , the micro-cracks gradually develop and converge with the increase of axial displacement, and finally form the main oblique cracks with an angle of about 60° to the loading direction. When the axial compressive stress σ drops to 0.95f c , the axial compressive stress rapidly decreases, and the specimen enters the failure stage. The test phenomena of coal gangue aggregate concrete specimens are similar to those of ordinary concrete. During the failure process of the specimen, fine branch cracks form beside the main cracks, which slowly expand with the increase of axial deformation.

[0108] The typical failure mode of the concrete specimen is shown in Figure 4 . As can be seen from Figure 4 , the coal gangue aggregate does not change the failure mode of the concrete, and all specimens show shear failure. In the CGAC-C100-F100-0.55 specimen, it can be seen that due to the weakening of the constraint effect of coal gangue aggregate on crack development, obvious cracks form near the main cracks. In the CGAC-C100-F100-0.35 specimen, due to the low strength of coal gangue aggregate, cracks appear through the aggregate, resulting in a significant change in the angle of the oblique main cracks.

[0109] 2 Peak stress

[0110] Figure 5 The variation of the peak stress of the concrete specimen under different water-cement ratios is compared, which is influenced by the replacement rate of coal gangue coarse aggregate and coal gangue fine aggregate, wherein w / c represents the water-cement ratio, r c represents the replacement rate of coarse aggregate, and r f represents the replacement rate of fine aggregate. From Figure 5As can be seen, the addition of both coarse and fine coal gangue aggregates reduces the peak stress of concrete. For example, compared to ordinary concrete, when only coarse coal gangue aggregate is used, the peak stress of coal gangue aggregate concrete decreases by 5.6% to 23.9%; while when only fine coal gangue aggregate is used, the peak stress decreases by 8.1% to 20.8%. Complete replacement of natural aggregates with coal gangue aggregates reduces the peak stress of concrete by 26.5% to 34.9%. This is because the strength of both coarse and fine coal gangue aggregates is lower than that of natural coarse and fine aggregates. Under axial compression, the weakening effect of coal gangue aggregates on peak stress becomes more pronounced as the replacement rate increases.

[0111] The effect of coal gangue aggregate on the peak stress of concrete is significantly influenced by the water-cement ratio. When only the coarse coal gangue aggregate replacement rate is 100%, compared with ordinary concrete, the peak stress of the coal gangue aggregate concrete specimen with a water-cement ratio of 0.55 decreased by 5.55%, but at a water-cement ratio of 0.35, this value reached 23.9%. Similarly, when only the fine coal gangue aggregate replacement rate is 100%, the peak stress of the coal gangue aggregate concrete specimen with a water-cement ratio of 0.55 decreased by 8.08% compared with ordinary concrete, while at a water-cement ratio of 0.35, this value was 20.8%. This is due to the strength difference between cement paste and coal gangue aggregate. Specifically, in concrete with a high water-cement ratio, the strength difference between cement paste and coal gangue aggregate is not significant; however, when the water-cement ratio of concrete is reduced, the strength of cement paste increases, which increases the strength difference between coal gangue aggregate and cement paste, ultimately leading to a more significant decrease in peak stress in concrete with a low water-cement ratio.

[0112] In this invention, the ratio of axial compressive strength to cubic compressive strength of coal gangue aggregate concrete, measured under different water-cement ratios and with single or compound admixtures of coarse and fine coal gangue aggregates, is close to that of ordinary concrete. For coal gangue aggregate concrete, this ratio increases by -9.4% to 14.8% compared to ordinary concrete, and is not significantly correlated with the water-cement ratio or the replacement rate of coarse and fine coal gangue aggregates. According to previous research, this ratio increases by -18.9% to 25.2% compared to natural concrete. Therefore, within this range, the ratio of axial compressive strength to cubic compressive strength of coal gangue aggregate concrete in this experiment is consistent with that of ordinary concrete.

[0113] 3 Transverse deformation coefficient

[0114] This experiment measured the development trend of the transverse deformation coefficient of the concrete specimen during loading, such as... Figure 6 As shown. Figure 6 The development curve of the transverse deformation coefficient is the average value of the test results of three specimens in the same group. It can be seen that when the longitudinal strain... When the value is less than 1000με, the concrete is in the elastic stage. The water-cement ratio and the amount of coal gangue aggregate have an effect on the transverse deformation coefficient of the concrete specimen. The impact is relatively small, all around 0.2 (with a difference of no more than 11.1%).

[0115] When the longitudinal strain is between 1000με and 2000με, the specimen enters the plastic stage. The development trend of the transverse deformation coefficient of coal gangue aggregate concrete with a water-cement ratio of 0.55 is significantly faster than that of ordinary concrete. Conversely, there is no significant difference in the development trend of the transverse deformation coefficient between coal gangue aggregate concrete with a water-cement ratio of 0.35 and ordinary concrete.

[0116] The significant difference in the development trend of the transverse deformation coefficient is mainly due to the faster initiation and development of cracks in coal gangue aggregate concrete compared to ordinary concrete. Specifically, under axial compression, the development of concrete cracks is closely related to the fracture energy. When the local accumulated energy in the concrete reaches the fracture energy, cracks begin to develop. For coal gangue aggregate concrete, the lightweight and porous nature of coal gangue reduces its constraint on crack development, leading to a smaller fracture zone width and thus a lower fracture energy. This manifests as faster crack development, more microcracks, and ultimately an increased transverse deformation coefficient. However, after reducing the water-cement ratio, the cement paste and coal gangue aggregate are more tightly bonded, resulting in improved shear resistance and less transverse deformation.

[0117] 4 Peak strain

[0118] Figure 7 The influence of coal gangue aggregate on the peak strain of concrete under different water-cement ratios was analyzed. Figure 7 As can be seen, the peak strain of concrete increases with the increase in the replacement rate of coal gangue aggregate. For example, in the case of dual admixture of coal gangue aggregate, a 100% replacement rate will increase the peak strain of concrete by 8.9% to 18.9%. This is mainly due to the lower stiffness of coal gangue aggregate. Under axial load, the lower stiffness of coal gangue aggregate will cause greater deformation than the higher stiffness of natural aggregate, thus increasing the peak strain of concrete.

[0119] from Figure 7It can also be seen that the influence of coal gangue aggregate on the peak strain of concrete increases with the increase of water-cement ratio. For example, compared with ordinary concrete, the peak strain of coal gangue aggregate concrete with a water-cement ratio of 0.35 increases by 8.36% when only containing coal gangue fine aggregate, and the peak strain of coal gangue aggregate concrete with a water-cement ratio of 0.55 increases by 28.8%. This is caused by the low strength and small stiffness of coal gangue aggregate. Specifically, the peak strain of concrete is composed of the peak strain of aggregate and the peak strain of cement paste. When the concrete reaches the peak stress, the aggregate usually only has elastic strain, and the cement paste has a large plastic strain in addition to the elastic strain. At a high water-cement ratio, the peak stress of coal gangue aggregate concrete is not significantly lower than that of ordinary concrete. In this case, the low stiffness of coal gangue aggregate mainly causes the significant increase of the peak strain of concrete. At a low water-cement ratio, the low strength of coal gangue aggregate leads to a significant decrease in the peak stress of coal gangue aggregate concrete, and the plastic strain of the cement paste in the coal gangue aggregate concrete is smaller than that of the cement paste in the ordinary concrete, finally showing that the peak strain of the coal gangue aggregate concrete does not significantly increase.

[0120] 5Deformation capacity

[0121] When the axial compressive stress σ decreases to 1 / 2 of the peak stress after reaching the peak stress, the corresponding limit strain is the key to describe the descending section of the axial compressive stress-strain relationship curve of concrete. Therefore, the deformation capacity of concrete in the present application is represented as the limit strain ε u divided by the peak strain ε0, and the result is shown in Figure 8 .

[0122] As can be seen from Figure 8 , the incorporation of coal gangue coarse aggregate and coal gangue fine aggregate will both reduce the deformation capacity of concrete. For example, when the coal gangue aggregate is used to replace 100% of the natural aggregate, the deformation capacity of concrete decreases by 8.23%-12.5%. This is because the deformation capacity of concrete is closely related to its fracture energy, and the higher the fracture energy, the stronger the deformation capacity of concrete. The low stiffness of coal gangue aggregate reduces its constraint on the development of cracks in concrete, and the cracks in coal gangue aggregate concrete are more likely to develop than those in ordinary concrete, and the fracture zone width of coal gangue aggregate concrete is smaller than that of ordinary concrete, and thus the fracture energy of coal gangue aggregate concrete is also smaller than that of ordinary concrete, finally showing the decrease of the deformation capacity of concrete.

[0123] In Figure 8It can also be seen that the influence of coal gangue aggregate on the deformation capacity of concrete is less affected by the water-cement ratio. Taking the case of 100% replacement of coal gangue coarse aggregate, for the concrete with a water-cement ratio of 0.55, the influence results in a decrease of 4.8% in the deformation capacity compared with ordinary concrete; and for the concrete with a water-cement ratio of 0.35, the influence is 5.6%, which is similar to the former. This is because within the water-cement ratio range of the present application (0.35 and 0.55), the low rigidity of the coal gangue aggregate plays a major role in the influence on the deformation capacity of concrete. Specifically, the aggregate restricts the development of cracks in concrete by restricting the deformation of the cement paste, thereby affecting the deformation capacity of concrete. The rigidity of the coal gangue aggregate is significantly lower than that of natural aggregate, resulting in a significantly lower restriction on the deformation of the cement paste than natural aggregate at different water-cement ratios, and finally showing a similar decrease in the deformation capacity of concrete at different water-cement ratios.

[0124] Specific embodiment one: the present application provides a method for predicting the axial compression stress-strain relationship of coal gangue aggregate concrete, comprising the following steps:

[0125] Based on the ordinary concrete axial compression stress-strain relationship model recommended in the Concrete Structure Design Standard GB / T 50010-2010, the present application considers the influence of coal gangue aggregate and proposes an axial compression stress-strain relationship model for coal gangue aggregate concrete. From the test results of the present application and existing test results, it can be seen that coal gangue aggregate has a significant influence on the shape of the rising section, peak strain and shape of the descending section of the axial compression stress-strain relationship curve of concrete;

[0126] S100、To consider the above influences, the present application introduces elastic modulus correction coefficient k c,E , peak strain correction coefficient k c,ε and descending section shape parameter correction coefficient k c,α into the original axial compression stress-strain relationship formula, as shown in formula (1)~formula (3):

[0127]

[0128] wherein, represent the elastic modulus of coal gangue aggregate concrete and ordinary concrete, respectively;

[0129]

[0130] wherein, represent the peak strain of coal gangue aggregate concrete and ordinary concrete, respectively;

[0131]

[0132] wherein, represent the descending section shape parameter of coal gangue aggregate concrete and ordinary concrete, respectively.

[0133] The above correction coefficient is substituted into the ordinary concrete axial compression stress-strain relationship model to obtain the axial compression stress-strain relationship model of the coal gangue aggregate concrete, which is expressed by formula (4) to formula (8):

[0134]

[0135]

[0136] Wherein, σ represents the axial compression stress of the coal gangue aggregate concrete, and ε represents the axial compression strain of the coal gangue aggregate concrete; represents the peak stress of the coal gangue aggregate concrete;

[0137] S200, for the elastic modulus correction coefficient k c,E , the relationship between the elastic modulus of the coal gangue aggregate concrete and the elastic modulus of the ordinary concrete with the same mix proportion is obtained:

[0138]

[0139] Wherein, r CGCA is the replacement rate of the coal gangue coarse aggregate, r CGFA is the replacement rate of the coal gangue fine aggregate, is the volume fraction of the coal gangue coarse aggregate in the total aggregate; is the volume fraction of the coal gangue fine aggregate in the total aggregate;

[0140] S300, for the peak strain correction coefficient k c,ε , based on the Voigt model in the two-phase composite material theory, Figure 9 the relationship between the peak strain of the ordinary concrete and the peak strain of each component (i.e. the cement paste and the total aggregate) in the ordinary concrete can be obtained, and then the calculation formula of the peak strain correction coefficient (k c,ε ) of the coal gangue aggregate concrete is derived;

[0141] For ordinary concrete, the peak strain can be expressed by the peak strain of the total aggregate and the peak strain of the cement paste and the volume fraction of the total aggregate, as follows:

[0142]

[0143] In the formula, respectively represent the peak strain of the total aggregate and the cement paste when the axial stress reaches the peak stress of the ordinary concrete, με; V NA represents the volume fraction of the total aggregate in the ordinary concrete;

[0144] Similarly, the peak strain of the coal gangue aggregate concrete when the axial stress reaches the peak stress is The peak strain of total aggregate (including coal gangue aggregate and natural aggregate) and peak strain of cement paste in coal gangue aggregate concrete, as well as the volume fraction of total aggregate, can also be used to represent the concrete, as shown below:

[0145]

[0146] In the formula, ε represents the peak strain of the total aggregate and cement paste, respectively, when the axial stress reaches the peak stress of the coal gangue aggregate concrete. This indicates the volume fraction of total aggregate in coal gangue aggregate concrete.

[0147] During concrete loading, the aggregate does not undergo plastic deformation, therefore, in equation (12)... With equation (13) It can be calculated using equations (14) and (15) respectively.

[0148]

[0149] in, This represents the peak stress in ordinary concrete. It represents the stiffness of aggregates in ordinary concrete, that is, the elastic modulus of natural aggregates in ordinary concrete. Represents the peak stress of coal gangue aggregate concrete; It represents the stiffness of the total aggregate in coal gangue aggregate concrete, that is, the elastic modulus of the total aggregate in coal gangue aggregate concrete.

[0150] In coal gangue aggregate concrete, the total aggregate can be considered as a two-phase composite material of natural aggregate and coal gangue aggregate, and its stiffness can be calculated according to formula (16):

[0151]

[0152] Among them, E CGA The elastic modulus of coal gangue aggregate. The volume fraction of natural aggregate in coal gangue aggregate concrete.

[0153] According to the research of Kohees et al., the peak strain of cement paste has a significant linear correlation with its peak stress, which can be approximated by equation (17).

[0154]

[0155] in, This indicates the peak stress of the cement paste; This represents the peak strain of the cement paste, and ;

[0156] Since the effective water-cement ratio of the cement paste of the coal gangue aggregate concrete is similar to that of the ordinary concrete, the peak strain of the two kinds of cement paste can be calculated by formula (17). By substituting formula (14) and formula (17) into formula (12) and substituting formula (15) and formula (17) into formula (13), and considering that the coal gangue aggregate replaces the natural aggregate by volume, the expression of the peak strain correction coefficient of the coal gangue aggregate concrete can be obtained, as shown in formula (18):

[0157]

[0158] wherein, , is the volume fraction of the total aggregate in the concrete; is the peak stress of the ordinary concrete;

[0159] The peak strain test data of 37 groups of coal gangue aggregate concrete collected from 5 documents and the test results of the present application are used to verify the proposed model (formula (18)), and the results are shown in Figure 10 . Among them, the test results of the present application are represented by gray square marks. It can be seen from Figure 10 that the proposed model of the present application has high accuracy, and the linear regression coefficient of the ratio of the predicted value to the test value is 0.899, and the determination coefficient (R 2 ) is 0.977;

[0160] S400, for the descending segment shape parameter correction coefficient k c,α The shape of the descending segment of the stress-strain relationship curve of the concrete is closely related to the fracture energy of the concrete, therefore, the present application determines the descending segment shape parameter correction coefficient k by establishing the relationship between the fracture energy of the coal gangue aggregate concrete (G ) and the fracture energy of the ordinary concrete (G c,α );

[0161] Bazant et al. believe that the fracture zone width of the ordinary concrete is an important factor affecting the fracture energy thereof, and based on this, a fracture energy calculation model thereof is established, as shown below:

[0162]

[0163] In the formula, represents the fracture zone width of the ordinary concrete, mm; represents the elastic modulus of the ordinary concrete, GPa; represents the tensile strain softening modulus of the ordinary concrete, GPa; represents the tensile strength of the ordinary concrete, MPa;

[0164] Existing research and the experiments of this invention show that the compressive failure mechanism of coal gangue aggregate concrete is similar to that of ordinary concrete; at the same time, it is assumed that the ratio of the elastic modulus to the tensile strain softening modulus of coal gangue aggregate concrete is ( ) and ordinary concrete ( The values ​​are equal; therefore, this invention establishes a calculation model for the fracture energy of coal gangue aggregate concrete, as shown below:

[0165]

[0166] In the formula, The width of the fracture zone in coal gangue aggregate concrete, in mm; The elastic modulus of coal gangue aggregate concrete, expressed in GPa; The tensile strength of coal gangue aggregate concrete, expressed in MPa.

[0167] Dividing equation (20) by equation (19) yields the fracture energy amplification factor for coal gangue aggregate concrete. As shown in equations (21) to (23):

[0168]

[0169] In the formula, k c,d The correction factor for the fracture zone width of coal gangue aggregate concrete; k c,ft The tensile strength correction factor for coal gangue aggregate concrete; k c,E The elastic modulus correction factor represents the elastic modulus of coal gangue aggregate concrete;

[0170] In Equation (22), the fracture zone width of coal gangue aggregate concrete and ordinary concrete is a key parameter for calculating fracture energy; the maximum particle size of coarse aggregate in concrete affects the fracture zone width by influencing the crack propagation path, while the constraint effect of aggregate on crack propagation is related to the apparent density of concrete; based on this, a prediction model for the fracture zone width of ordinary concrete is established, as shown in Equation (24); similarly, a prediction model for the fracture zone width of coal gangue aggregate concrete can be established, as shown in Equation (25):

[0171]

[0172] In the formula, The benchmark apparent density of concrete can be taken as 2300 kg / m³. 3 ; The apparent density of ordinary concrete and coal gangue aggregate concrete, in kg / m³. 3 X1 and X2 represent regression coefficients; This represents the maximum particle size of coarse aggregate in ordinary concrete. This represents the maximum particle size of coarse aggregate in coal gangue aggregate concrete.

[0173] Substitute formula (24) and formula (25) into formula (22), we can get:

[0174]

[0175] When the coarse aggregate in the ordinary concrete and the coal gangue aggregate concrete use the same mix proportion, the maximum particle size of the coarse aggregate can be considered to be similar, that is, ≈1, formula (26) can be simplified as formula (27):

[0176]

[0177] Since the coal gangue aggregate concrete and the ordinary concrete use the same mix proportion, and the coal gangue aggregate in the coal gangue aggregate concrete replaces the natural aggregate in the form of volume replacement, the aggregate volume and the cement paste volume of the two are equal, so we get:

[0178]

[0179] In the formula, represents the weighted apparent density of the aggregate in the ordinary concrete; represents the weighted apparent density of the aggregate in the coal gangue aggregate concrete; p cp represents the apparent density of the cement paste; represents the volume fraction of the aggregate in the concrete;

[0180] In the common mix proportion, the volume fraction of the aggregate is usually greater than that of the cement paste, so the apparent density of the aggregate in the concrete can reflect the apparent density of the concrete to a certain extent; and the existing research on the axial compressive stress-strain relationship of the coal gangue aggregate concrete mostly only gives the apparent density of the aggregate; in order to make full use of the existing test data, the ratio of the weighted apparent densities of the aggregates is considered to be approximately replaced by the ratio of the apparent densities of the concretes, and finally the expression of the correction coefficient of the fracture zone width of the coal gangue aggregate concrete is obtained, as shown below:

[0181]

[0182] In the formula, X3 represents the regression coefficient;

[0183] The weighted apparent density of the aggregate in the concrete can be calculated by the volume fraction of the coarse aggregate and the fine aggregate; further, considering the replacement rate of the coal gangue coarse aggregate and the coal gangue fine aggregate, the weighted apparent density of the aggregate in the coal gangue aggregate concrete can be calculated, as shown in formula (30) to formula (32); when the replacement rate of the coal gangue coarse aggregate and the coal gangue fine aggregate is 0%, the weighted apparent density of the aggregate in the ordinary concrete calculated by formula (30) is:

[0184]

[0185] where, ρ CGCA , ρ NCA represent the apparent density of coal gangue coarse aggregate and natural coarse aggregate, kg / m 3 ; ρ CGFA , ρ NFA represent the apparent density of coal gangue fine aggregate and natural fine aggregate, kg / m 3 ;

[0186] According to the previous research results on the calculation of fracture energy, the calculation expression of the shape parameter of the concrete descending section is as formula (33):

[0187]

[0188] According to the data of 37 groups in 5 literatures , different k c,d values are calculated, and through regression analysis, the value of regression coefficient X3 in formula (29) is 16.0;

[0189] The test data of deformation capacity (ε u / ε0) of 37 groups of coal gangue aggregate concrete collected from 5 literatures and the test results of the present application are used to verify the proposed model (formula (33)), and the results are shown in Figure 11 . In which, the test results of the present application are represented by gray square marks. From Figure 11 , it can be seen that the prediction accuracy of the proposed model of the present application is high, the linear regression coefficient is 0.974, and the determination coefficient (R 2 ) is 0.985.

[0190] Model verification

[0191] The axial compression stress-strain relationship model (formula (4)~formula (8)) of coal gangue aggregate concrete proposed by the present application is verified by 31 groups of coal gangue aggregate concrete tests in 5 literatures and the test of the present application, and the results are shown in Figures 12-17 . The parameters of the test data used include coal gangue coarse aggregate, coal gangue fine aggregate replacement rate (0%~100%), and concrete 28-day compressive strength (18.6MPa~59.3MPa), which can cover the strength range of common concrete. The existing test data includes common coal gangue aggregate pretreatment methods, such as saturated face dry method , additional water compensation method , and pre-wetting method . A total of 45 groups of test data are collected, and the test parameter range is wide, corresponding to ordinary concrete strength grades C30~C55, coal gangue coarse aggregate replacement rate 0%~100%, and coal gangue fine aggregate replacement rate 0%~100%, and the determination coefficient R 20.95 and 0.96, respectively, verifying the reliability of the model.

[0192] Specific implementation two: the present application is a kind of coal gangue aggregate concrete axial stress-strain relationship prediction system, the system has the program module corresponding to the above steps, when running, the steps in the above application are executed in the improved heuristic static path planning method for mobile robot.

[0193] Other combinations and connection relationships of the present embodiment are the same as specific implementation one.

[0194] Specific implementation three: the present application is a kind of computer readable storage medium, the computer readable storage medium stores computer program, the computer program is configured to be called by processor to realize the steps of a kind of coal gangue aggregate concrete axial stress-strain relationship prediction method.

[0195] Other combinations and connection relationships of the present embodiment are the same as specific implementation one.

[0196] Although the present application is disclosed as above, the protection scope of the present application is not limited to this. The person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application, and these changes and modifications will fall within the protection scope of the present application.

[0197] [1] ZHOU M, DOU Y, ZHANG Y, et al. Effects of the variety and content of coal gangue coarse aggregate on the mechanical properties of concrete [J]. Construction and Building Materials, 2019, 220: 386-395.

[0198] [2] ZHANG T, WEN Q, GAO S, et al. Comparative study on mechanical and environmental properties of coal gangue sand concrete [J]. Construction and Building Materials, 2023, 400.

[0199] [3] DONG W, REN Z, LIU X. Experimental study on constitutive relation of coal gangue coarse aggregate concrete under uniaxial compression [J]. Materials Today Sustainability, 2024, 28.

[0200] [4] ZHANG Y, WANG Q, ZHOU M, et al. Mechanical properties of concrete with coarse spontaneous combustion gangue aggregate (SCGA): Experimental investigation and prediction methodology [J]. Construction and Building Materials, 2020, 255.

[0201] [5] LIU H, BAI G, GU Y, et al. The influence of coal gangue coarse aggregate on the mechanical properties of concrete columns [J]. Case Studies in Construction Materials, 2022, 17.

Claims

1. A method of predicting the stress-strain relationship of coal gangue aggregate concrete under axial compression, characterized by, The method comprises the following steps: S100、In the axial stress-strain relationship formula, the elastic modulus correction coefficient k is introduced c,E , the peak strain correction coefficient k c,ε And the shape parameter correction coefficient k of the descending section c,α , the axial stress-strain relationship model of coal gangue aggregate concrete is obtained; S200、For elastic modulus correction coefficient k c,E , the elastic modulus of the coal gangue aggregate concrete and the elastic modulus of the ordinary concrete with the same mix proportion are obtained. S300、for peak strain correction coefficient k c,ε Based on the Voigt model in the two-phase composite material theory, the relationship between the peak strain of concrete and the peak strain of each component in the concrete is obtained, and the calculation formula of the peak strain correction coefficient k c,ε of coal gangue aggregate concrete is derived. S400, for the descending segment shape parameter correction coefficient k c,α , the descending segment shape parameter correction coefficient k is determined by establishing the relationship between the coal gangue aggregate concrete fracture energy and the ordinary concrete fracture energy c,α ; wherein, in order to calculate the fracture energy, a fracture zone width prediction model of the coal gangue aggregate concrete is constructed to obtain a calculation formula of the coal gangue aggregate concrete fracture zone width correction coefficient; the volume proportion of the coal gangue coarse aggregate, the coal gangue fine aggregate, the natural coarse aggregate and the natural fine aggregate in the concrete is used to calculate the weighted average apparent density, and finally the calculation formula of the descending segment shape parameter correction coefficient k c,α is obtained.

2. The method according to claim 1, wherein the method is characterized by: In step S100, an elastic modulus correction coefficient k is introduced c,E , a peak strain correction coefficient k c,ε , and a falling segment shape parameter correction coefficient k c,α , as shown in equations (1) to (3): ； wherein, respectively represent the elastic modulus of coal gangue aggregate concrete and ordinary concrete; ； wherein, respectively represent the peak strain of coal gangue aggregate concrete and ordinary concrete; ； wherein, respectively represent the shape parameters of the descending section of the coal gangue aggregate concrete and the ordinary concrete; The elastic modulus correction coefficient k c,E The peak strain correction coefficient k c,ε The shape parameter correction coefficient k c,α The axial compression stress-strain relationship model of coal gangue aggregate concrete is obtained by substituting the elastic modulus correction coefficient k c,E , the peak strain correction coefficient k c,ε and the shape parameter correction coefficient k c,α into the axial compression stress-strain relationship model of concrete, which is represented by equations (4)-(8). ； Wherein, σ represents the axial compressive stress of coal gangue aggregate concrete, and ε represents the axial compressive strain of coal gangue aggregate concrete. represents the peak stress of coal gangue aggregate concrete.

3. The method of claim 2, wherein the method is characterized by: In step S200, the elastic modulus correction coefficient k c,E : ； wherein r CGCA is the coal gangue coarse aggregate replacement rate, r CGFA is the coal gangue fine aggregate replacement rate, is the volume fraction of coal gangue coarse aggregate in total aggregate; is the volume fraction of coal gangue fine aggregate in total aggregate; is the volume fraction of total aggregate in concrete.

4. The method of claim 3, wherein the method is characterized by: In step S300, for ordinary concrete, the peak strain is expressed by the peak strain of the aggregate and the peak strain of the cement paste and the volume fraction of the aggregate: ； wherein respectively represent the peak strain of the aggregate and cement paste when the axial stress reaches the peak stress of ordinary concrete; V NA represents the volume fraction of total aggregate in ordinary concrete; Peak strain of coal gangue aggregate concrete when axial stress reaches peak stress It can also be expressed by the peak strain of total aggregate in coal gangue aggregate concrete and the peak strain of cement paste and the volume fraction of aggregate: ； In the formula, respectively represent the peak strain of the total aggregate and cement paste when the axial stress reaches the peak stress of the coal gangue aggregate concrete; represents the volume fraction of the total aggregate in the coal gangue aggregate concrete. The aggregate does not undergo plastic deformation during the loading of the concrete, so the term is calculated by Equations (14) and (15), respectively: is calculated by Equations (14) and (15), respectively: ； wherein, represents the peak stress of normal concrete; represents the stiffness of aggregate in normal concrete, i.e. the elastic modulus of natural aggregate in normal concrete; represents the peak stress of coal gangue aggregate concrete; represents the stiffness of total aggregate in coal gangue aggregate concrete, i.e. the elastic modulus of total aggregate in coal gangue aggregate concrete; Wherein, the total aggregate in the coal gangue aggregate concrete is a two-phase composite material of natural aggregate and coal gangue aggregate, and the stiffness is calculated according to formula (16): ； wherein E CGA is the elastic modulus of the coal gangue aggregate, is the volume fraction of natural aggregate in the coal gangue aggregate concrete; Since the peak strain of the cement paste has a significant linear correlation with the peak stress, it is approximately expressed by formula (17): ； wherein, represents the peak stress of the cement paste; represents the peak strain of the cement paste, and ; Finally, the coal gangue aggregate is replaced with natural aggregate by volume to obtain the expression of the peak strain correction coefficient of the coal gangue aggregate concrete, as shown in formula (18): （18）。 5. The method of claim 4, wherein the method is characterized by: In step S400, a calculation model of the fracture energy of the ordinary concrete is established based on the fracture zone width of the ordinary concrete : ； wherein represents the fracture zone width of the ordinary concrete; represents the elastic modulus of the ordinary concrete; represents the tensile strain-softening modulus of the ordinary concrete; represents the tensile strength of the ordinary concrete; Assuming that the ratio of the elastic modulus to the tensile strain-softening modulus of the coal gangue aggregate concrete is equal to that of the ordinary concrete ; thus, a calculation model for the fracture energy of the coal gangue aggregate concrete is established: ； In the formula, represents the fracture zone width of the coal gangue aggregate concrete; represents the elastic modulus of the coal gangue aggregate concrete; represents the tensile strength of the coal gangue aggregate concrete; Dividing equation (20) by equation (19) obtains the magnification coefficient of the coal gangue aggregate concrete fracture energy As shown in equations (21)-(23): ； wherein k c,d represents a correction coefficient of the fracture zone width of the coal gangue aggregate concrete; k c,ft represents a correction coefficient of the tensile strength of the coal gangue aggregate concrete; k c,E represents a correction coefficient of the elastic modulus of the coal gangue aggregate concrete; Based on the fact that the maximum particle size of the coarse aggregate in concrete affects the development path of the crack and thus affects the fracture zone width of the concrete, a prediction model of the fracture zone width of the coal gangue aggregate concrete is established: ； wherein, represents the reference apparent density of concrete; represents the apparent density of ordinary concrete and coal gangue aggregate concrete; X1, X2 represent regression coefficients; represents the maximum particle diameter of coarse aggregate in ordinary concrete; represents the maximum particle diameter of coarse aggregate in coal gangue aggregate concrete; Further, we have ； When the coarse aggregate in the ordinary concrete and the coal gangue aggregate concrete uses the same gradation, it is considered that the maximum particle size of the coarse aggregate is similar, that is Then, equation (26) is simplified to equation (27): ； Since the coal gangue aggregate concrete and the ordinary concrete use the same mix proportion, and the coal gangue aggregate in the coal gangue aggregate concrete replaces the natural aggregate by volume, the aggregate volume and the cement paste volume of the two are equal, and formula (25) is obtained: ； wherein ρa represents the weighted apparent density of the aggregate in the ordinary concrete; ρa represents the weighted apparent density of the aggregate in the coal gangue aggregate concrete; cp ρc represents the apparent density of the cement paste; ρa represents the volume fraction of the aggregate in the concrete; Considering that the ratio of the weighted apparent density of the aggregate is approximately replaced by the ratio of the apparent density of the concrete, the expression of the correction coefficient of the fracture zone width of the coal gangue aggregate concrete is finally obtained, as shown in formula (29): ； In the formula, X3 represents the regression coefficient; Considering the replacement rate of the coal gangue coarse aggregate and the coal gangue fine aggregate, the weighted apparent density of the aggregate in the coal gangue aggregate concrete is calculated, as shown in formula (30)-(32); when the replacement rate of the coal gangue coarse aggregate and the coal gangue fine aggregate is 0%, the weighted apparent density of the aggregate in the ordinary concrete is calculated by formula (30): ； In the formula, p CGCA , p NCA represents the apparent density of coal gangue coarse aggregate and natural coarse aggregate; p CGFA , p NFA represents the apparent density of coal gangue fine aggregate and natural fine aggregate; Finally, the calculation expression of the shape parameter of the descending section of the concrete is: （33）。 6. A system for predicting the stress-strain relationship of coal gangue aggregate concrete under axial compression, characterized in that: The system has program modules corresponding to the steps of any one of claims 1-5, and when running, the steps of the improved heuristic static path planning method for mobile robots are executed.

7. A computer-readable storage medium, characterized in that: The computer readable storage medium stores a computer program configured to realize the steps of the prediction method of the stress-strain relationship of the coal gangue aggregate concrete according to any one of claims 1-5 when called by the processor.

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